This invention is in the technical field of nuclear magnetic resonance (NMR) and more particularly relates to an NMR probe capable of generating an optimized RF magnetic field orthogonal to a polarizing field for study of a sample rotating about an axis oriented at a specified angle from the direction of the polarizing field.
It has been known in the analysis by magnetic resonance to rotate a sample at a high speed xcfx89s in a uniform magnetic polarizing field around a sample rotation axis directed along a selected angle xcex8 from the direction of this polarizing field (B0) to average over dipolar couplings in the sample and to average over spatial inhomogeneities of the sample. The selected angle is frequently the so-called magic angle, which is defined as the zero of the function 3 cos2 xcex8xe2x88x921, or about 54xc2x0 44xe2x80x2.
In order to achieve a desired distribution of RF magnetic field (B1) over the volume of the sample, it has been known to provide a solenoidal coil with the coil former support structure oriented on the axis of rotation of the sample (or the sample container). Consider FIG. 1. The RF magnetic field B1s generated by such a solenoidal coil (represented here by resonator 8) is in the direction of the axis of rotation 9 but it is the component of this field perpendicular to the polarizing field B0 that is of importance in NMR applications, that is, the projection of B1s on the x-y plane. For simplicity, let the rotation axis be in the z-y plane and let the angle between the direction of the polarizing field B0, and the axis of rotation (solenoid axis) be xcex8 and the RF phase for the solenoid is xcfx81s. It follows that
B1sB1ssin xcex8 cos(xcfx89t+xcfx81s)Y+B1s cos xcex8 cos(xcfx89t+xcfx81s)Z
The effective field component due to the solenoid is limited to the projection onto the x-y plane and thus will be
B1seffective=B1s sin xcex8 cos(xcfx89t+xcfx81s)Yxe2x80x83xe2x80x83(Equ.1)
If xcex8 is the magic angle, the effective field will be about 0.816B1 for such prior art.
It is desired to increase the B1 field available for manipulation of nuclear spins and to increase the signal-to-noise ratio for resonance detection when an axially symmetric probe coil is inclined with respect to B0. It is known to produce an RF field at a small angle with respect to the solenoidal axis of a solenoidal RF coil by tilting the approximate plane (of a current loop) to the solenoidal axis. The B1seffective vector resulting from this known arrangement is approximately inclined by the tilt angle with respect to the axis of the coil support. However, the vector is smeared over a cone (cone-angle equal to the tilt angle) in accordance with the distribution of normals to the non-coplanar surface enclosed by the current xe2x80x9cloopxe2x80x9d.
It is therefore an object of this invention to provide more effective RF coils for a spinning probe which may be oriented at a selected angle with respect to the static field and in particular, at the magic angle.
Saddle coil and birdcage coil geometries each produce an RF magnetic field in the plane perpendicular to their geometric symmetry axis which may be identified with the solenoidal/sample rotation axis.
A birdcage coil having a pair of angularly displaced RF ports, each tuned to the same resonance frequency produces (on excitation) a plane polarized RF magnetic field. Where the two amplitudes are equal, the angular displacement is 90xc2x0 and the phase difference is xcfx80/2, the polarization will be circular in the median plane of the birdcage coil. (The present invention is not limited to quadrature mode/circular polarization; in some cases, elliptical polarization may be desirable, in order to produce circular polarization projected onto the x-y plane). For simplicity, reference to circular polarization is intended to comprehend elliptical polarization and quadrature mode is representative of multi-mode coils in general.) A quadrature birdcage coil disposed with its axis oriented at xcex8 with respect to a polarizing field B0 along Z is again identifiable with resonator 8 of FIG. 1. The analysis is simplified if the rotation axis is again assumed to lie in the z-y plane and the two (quadrature) modes are of equal amplitude and characterized by phases xcfx81B and xcfx81B+xcfx80/2.
B1B=B1B cos(xcfx89t+xcfx81B)X(first mode)+[B1B cos xcex8 cos(xcfx89t+xcfx81B+xcfx80/2)Y+B1B sin xcex8 sin(xcfx89t+xcfx81B+xcfx80/2)Z](second mode)
Noting that only the X and Y contribute to NMR excitation phenomena, one has
B1Beffective=B1B cos(xcfx89t+xcfx81B)X+B1B cos xcex8 cos(xcfx89t+xcfx81B+xcfx80/2)Yxe2x80x83xe2x80x83(Equ. 2)
and these two terms are identified with the RF magnetic field components (oscillating in the plane P). The plane of polarization for the birdcage coil is that plane orthogonal to its cylindrical axis and will be referenced where appropriate as the P plane. Relaxing the condition of equal amplitudes for the two modes, one obtains an elliptically polarized wave in the plane P. With an appropriate choice of these amplitudes the elliptical polarization on the plane P will be projected onto the x-y plane as a circularly polarized wave, as discussed below.
A saddle coil may be disposed with its symmetry axis directed at an angle to B0. A single saddle coil produces linear polarization in the plane transverse to the inductive members of the coil, that is, transverse to the symmetry axis of the coil. The saddle coil may be rotated about its geometric axis to orient the polarization axis in a plane orthogonal to B0 whereby the RF magnetic field is optimized for a desired sample rotation axis orientation.
Plane polarized or linearly polarized RF fields may be vectorialy added to a solenoidal field to produce a resultant RF magnetic vector exhibiting a greater projection on the plane orthogonal to the uniform field B0 as compared to the solenoidal field component alone. The greater RF field projection on the x-y plane, orthogonal to B0, is more efficacious for NMR excitation and the same features which allow this greater coupling to the sample on excitation also promotes a closer coupling to the resonant de-excitation of the sample.
A spinning NMR probe according to this invention may be characterized as comprising not only a container for containing a sample, and means for rotating the container around an axis of rotation which makes a specified non-zero angle (such as the magic angle) but also a saddle coil resonator or a multi-mode resonator disposed around the sample and arranged along the axis of rotation of the sample container and means for exciting the saddle coil or multi-mode resonator to thereby provide a resultant B1 field having a major component perpendicular to the axis of rotation. In most familiar NMR applications the multi-mode resonator is represented by a quadrature coil and reference to quadrature coils throughout this work should be understood to include more general multi-mode coils where applicable. The quadrature coil may be a paraxial birdcage coil with rungs extending parallel to its central axis. Where such a coil is employed with quadrature detection/excitation, instead of a solenoid coil according to the prior art, the B1(P) field generated thereby is perpendicular to its symmetry axis(also the axis of rotation of the sample container). The B1(P) field of the present invention is characterized by a rotating vector (circularly or elliptically polarized field) rotating in the plane P transverse to the inductors of the quadrature coil.
In certain embodiments of the present invention, the vector B1(P) rotating in plane P or oscillating along an axis in plane P, couples to another vector B1(S), e.g., an axial field tuned to the same resonance frequency with a selected phase difference to B1(P) to produce a resultant B1. Assume that B1(P) and B1(S) are orthogonal. In the most general case, the tip of this resultant vector describes a 3D Lissajous figure of considerable complexity. Much complexity is removed when the frequencies of the two components are equal, as in the present invention. Where a saddle coil provides the RF field in the plane P, B1(P) is linearly polarized along a selected axis in P and in conjunction with an axial field -B1(S)- the tip of the resultant vector executes a 2D Lissajous figure in the plane containing the solenoidal axis and the magnetic axis of the saddle coil. Altogether, for the invention, the total effective RF magnetic field comprising vectors B1(S) coupled to B1(P) will be greater than 0.816B1 of prior art utilizing a simple solenoid oriented at the magic angle. The measure of efficacy for magnetic resonance is the relative magnitude of the RF field component of B1 which lay in that plane to which the polarizing field B0 is normal. It is when the RF magnetic field B1 is realized from a resonator inclined at some angle with respect to B0 that such B1 field is also inclined and presents some component parallel to B0 and this parallel component is ineffective for resonance excitation. In order to maximize resonance excitation, it is desired to maximize the projection of B1 on the x-y plane that is orthonormal to B0.
Two coils producing orthogonally oriented RF magnetic field components at frequency xcfx890 may be combined to form an NMR probe for generating an RF field having components at selected orientations. A birdcage coil as described above in combination with a solenoid disposed coaxially, with one coil disposed inside the other, will provide such selected RF field orientations. A straightforward generalization of equ.2 is obtained for addition of an RF field from a solenoid oriented along an axis xcex8 inclined from z (and for notational convenience in the y-z plane) by adding the component of the solenoidal field, B1s, projected on y:
B1total=B1B cos(xcfx89t+xcfx81B)X+B1B cos xcex8 cos(xcfx89t+xcfx81B+xcfx80/2)Y+B15 sin xcex8 sin(xcfx89t+xcfx81s)Yxe2x80x83xe2x80x83(Equ.3)
In this case, the birdcage coil provides two orthogonal RF modes and the solenoid provides a third RF mode. Three distinct RF ports may be derived from such a probe forming three channels which may, for example, be connected to three parallel RF sources, or receivers for simultaneous (parallel) excitation, or detection.
A coaxial combination of saddle coil and solenoid coil is another example of the invention.
According to another, single coil embodiment of the invention, the quadrature coil is a birdcage coil of a skewed, or spiral geometry with rungs spiraling around its center axis where each skewed turn defines a normal vector making the same non-zero angle with the axis of rotation as the angle between the axis of rotation with the direction of the magnetic field B0. The two quadrature modes are then both perpendicular to the magnetic field B0 whereby the greatest geometric efficacy is obtained. The skewed geometry provides an axial component whereby the single birdcage coil produces the characteristically large volume homogeneous RF field at a selected orientation to the polarizing field with enhanced resonance coupling to the sample.
A probe in a multiple-tuned configuration may be formed with multiple-tuned coils, say, with a paraxial birdcage coil disposed at a tilted angle with respect to the magnetic field B0 coaxially disposed inside another birdcage coil of the skewed rung variety as described above.
More generally, a probe according to this invention may be formed with any two orthogonal B1 coils such as a saddle coil and a solenoid coil, both coils having common resonance properties and selected phase difference.